MASTER Sciences, Technologies, Santé MENTION Physique fondamentale et applications PARCOURS Physique fondamentale - Modèles non linéaires en physique
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> Responsable du Master 1 : Sergey SOLODUKHIN
> Responsable du Master 2 : Mikhail VOLKOV
Détails
Campagne de candidature
- du 22 mars au 18 avril 2023
plateforme mon master
- Dates à définir
Renseignements pratiques
- Structure(s) de rattachement
- Durée de la formation
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- 2 ans
- Formation continue
- Formation diplômante
- Lieu(x) de la formation
- Tours
- Stage(s)
- Oui, obligatoires
- Langues d'enseignement
-
Français
Accessible en
formation initiale, formation continue
Les + de la formation
Statistiques
Résultats 2021/2022Taux de réussite des présents aux examens
M1 Physique fondamentale - modèles non linéaires en physique
Effectifs 2022-2023 : 17
Taux de réussite 2021-2022 : 60 %
M2 Physique fondamentale - modèles non-linéaires en physique
Effectifs 2022-2023 : 5
Taux de réussite 2021-2022 : 100 %
> Toutes les statistiques
Numéro RNCP
N°RNCP : 31808Présentation
- former des étudiants attirés par les disciplines fondamentales de la physique telles que la physique quantique, la physique statistique, la physique des particules, la théorie classique des champs, la physique des solides.
Spécificités
- Maîtriser des théories de la physique fondamentale : la Relativité Générale et la cosmologie, la théorie quantique des champs, la physique des solitons, la théorie des systèmes dynamiques, etc
- Maîtriser des outils mathématiques
- Maîtriser des codes et logiciels de modélisation et simulation
- Avoir une méthode scientifique
Lieux
Tours
Responsable(s) de la formation
> Responsable du Master 1 : Sergey SOLODUKHIN
> Responsable du Master 2 : Mikhail VOLKOV
Admission
Niveau(x) de recrutement
Formation(s) requise(s)
Public ciblé
- Compétences et savoirs équivalents à ceux d’un titulaire d’une licence mention Physique à orientation Fondamentale
- Des résultats satisfaisants dans les enseignements correspondants à la dominante du M1 parcours Fondamental (en particulier : une bonne maîtrise des outils mathématiques d’un niveau Licence 3 en Physique ainsi que des connaissances solides en relativité restreinte et en mécanique quantique)
Candidature
Modalités de candidature
Modalités de traitement des candidatures :
- Dossier
Critères d’examens des dossiers :
- Titulaire d’une licence acceptée
- Résultats satisfaisants dans les enseignements correspondants à la dominante du M1 parcours Fondamental (en particulier : résultats satisfaisants requis en outils mathématiques, relativité restreinte et mécanique quantique)
- Niveau d’entrée en français C1 et niveau d’anglais B1
- Motivation pour la filière d’études
- Projet professionnel en cohérence avec le M1.
MASTER 2 : Candidature sur ecandidat via la procédure de validation des acquis ou de vérification des acquis
Modalités de candidature spécifiques
Étudiant étranger hors Union Européenne : Accédez au portail international de l'université
Formation continue et reprise d'études : Ce Master est également accessible dans le cadre de la formation continue (salariés, demandeurs d'emploi ou personnes sans activité) avec éventuellement des validations d'acquis.
- Plus d'informations sur le site de la formation continue
Programme
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Semestre 7 SM1NLP
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Semestre 8 SM1NLP
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Semestre 9 SM2NLP
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- CM UE1 Intro. to the theory and applications of S9 SM2NLP (Cours Magistral)15 h
- TD UE1 Intro. to the theory and applications of S9 SM2NLP (Travaux Dirigés)10 h
CM UE1 Intro. to the theory and applications of S9 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE1 Intro. to the theory and applications of S9 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE2 collective effects in quantum physics S9 SM2NLP (Cours Magistral)15 h
- TD UE2 collective effects in quantum physics S9 SM2NLP (Travaux Dirigés)10 h
CM UE2 collective effects in quantum physics S9 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE2 collective effects in quantum physics S9 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE3 Solitons un field theory S9 SM2NLP (Cours Magistral)15 h
- TD UE3 Solitons un field theory S9 SM2NLP (Travaux Dirigés)10 h
CM UE3 Solitons un field theory S9 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE3 Solitons un field theory S9 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE4 General relativity S9 SM2NLP (Cours Magistral)15 h
- TD UE4 General relativity S9 SM2NLP (Travaux Dirigés)10 h
CM UE4 General relativity S9 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE4 General relativity S9 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE5 Dynamical Systems S9 SM2NLP (Cours Magistral)15 h
- TD UE5 Dynamical Systems S9 SM2NLP (Travaux Dirigés)10 h
CM UE5 Dynamical Systems S9 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE5 Dynamical Systems S9 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE6 Numerical simulations S9 SM2NLP (Cours Magistral)15 h
- TD UE6 Numerical simulations S9 SM2NLP (Travaux Dirigés)10 h
CM UE6 Numerical simulations S9 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE6 Numerical simulations S9 SM2NLP
Travaux Dirigés 10 h
En savoir plus
UE1 Introduction to the theory and applications of S9 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the methods of integration of partial differential equations admitting soliton solutions.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: general knowledge of physics
Topics of the course: Non-linear waves, effects of dispersion and dissipation, solitary waves. Lattice solitons, Toda chain, the Fermi-Pasat-Ulam phenomenon, spin waves. Hydrodynamical solitons, equations of Kordeweg-de Vries and sin-Gordon, solitons in optical fibers. Mathematical aspects – the Lax formulation and the inverse scattering method.
Skills to be achieved:
Understanding the general notion of soliton.
Ability to integrate partial differential equations of certain types.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE2 collective effects in quantum physics S9 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the quantum-mechanical N-body problem and Green function method.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: quantum mechanics, statistical physics.
Topics of the course: Ground state and elementary excitations, quaziparticles and effective low-energy theories. Green functions at zero temperature, spectral representation, self-energy,
Green functions at finite temperature, Matsubara representation. Perturbation theory, S-matrix, Feynman diagrams. Models of Heisenberg and Hubbard, t-J model, sigma-model.
Skills to be achieved:
Understanding the perturbative description of interactions in quantum mechanics.
Understanding the collective effect description.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE3 Solitons un field theory S9 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the relativistic theory of solitons.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: classical field theory
Topics of the course: Scalar field theories in one dimension, topological charge, the phi^4 and
sin-Gordon models, Bogomol'nyi bound. Derrick theorem, sigma-model, topological solitons. Abelian Higgs model, Higgs mechanism, Meissner effect, vortices. Skyrme model, Yang-Mills theory, magnetic monopoles of Dirac and of t'Hooft-Polyakov. Weinberg-Salam theory.
Skills to be achieved:
Understanding mechanisms giving rise to stable lumps of energy in field theory.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE4 General relativity S9 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to Einstein's theory of gravity.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: classical field theory
Topics of the course: Elements of differential geometry: manifolds, metric, connections, curvature, Lie derivative, Killing vectors. Einstein equations, classical tests, massive spherical bodies, gravitational collapse. De Sitter space, Friedmann-Robertson-Walker metric. Axially symmetric metrics, initial value problem.
Skills to be achieved:
Understanding the basic principles of Einstein's theory.
Ability to handle the Einstein equations in simple cases.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE5 Dynamical Systems S9 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the basic notion of the theory of dynamical systems.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: general knowledge of physics
Topics of the course: Autonomous differential equations, fixed points and periodic orbits, Poincare-Bendixon theorem, theory of bifurcations. Linearization, Lyapunov exponents, stable and unstable manifolds. Hamiltonian systems, phase space, invariant tori, action-angle variables, problem of small denominators, the KAM theorem, application to the motion of asteroids. Dissipative systems, chaos, attractors, fractal dimensions.
Skills to be achieved:
Understanding the basic principles of the dynamical system approach.
Ability to qualitatively analyze a simple dynamical system.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE6 Numerical simulations S9 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Numerical simulations of molecular dynamics and the Monte-Carlo method.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: general knowledge of physics
Topics of the course: Molecular dynamics, discretization of the equations of motion, boundary conditions, thermalization. Monte-Carlo method, Metropolis algorithm, optimization problems.
Skills to be achieved:
Ability to simulate molecular dynamics using the C-language.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
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Semestre 10 SM2NLP
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- CM UE1 Systems of electrons S0 SM2NLP (Cours Magistral)15 h
- CM UE1 Systems of electrons S0 SM2NLP (Cours Magistral)15 h
- TD UE1 Systems of electrons S0 SM2NLP (Travaux Dirigés)10 h
- TD UE1 Systems of electrons S0 SM2NLP (Travaux Dirigés)10 h
CM UE1 Systems of electrons S0 SM2NLP
Cours Magistral 15 h
En savoir plusCM UE1 Systems of electrons S0 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE1 Systems of electrons S0 SM2NLP
Travaux Dirigés 10 h
En savoir plusTD UE1 Systems of electrons S0 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE2 Introduction to astrophysics and cosmology S0 SM2NLP (Cours Magistral)15 h
- CM UE2 Introduction to astrophysics and cosmology S0 SM2NLP (Cours Magistral)15 h
- TD UE2 Introduction to astrophysics and cosmology S0 SM2NLP (Travaux Dirigés)10 h
- TD UE2 Introduction to astrophysics and cosmology S0 SM2NLP (Travaux Dirigés)10 h
CM UE2 Introduction to astrophysics and cosmology S0 SM2NLP
Cours Magistral 15 h
En savoir plusCM UE2 Introduction to astrophysics and cosmology S0 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE2 Introduction to astrophysics and cosmology S0 SM2NLP
Travaux Dirigés 10 h
En savoir plusTD UE2 Introduction to astrophysics and cosmology S0 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE3 Introduction to quantum field theory S0 SM2NLP (Cours Magistral)15 h
- CM UE3 Introduction to quantum field theory S0 SM2NLP (Cours Magistral)15 h
- TD UE3 Introduction to quantum field theory S0 SM2NLP (Travaux Dirigés)10 h
- TD UE3 Introduction to quantum field theory S0 SM2NLP (Travaux Dirigés)10 h
CM UE3 Introduction to quantum field theory S0 SM2NLP
Cours Magistral 15 h
En savoir plusCM UE3 Introduction to quantum field theory S0 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE3 Introduction to quantum field theory S0 SM2NLP
Travaux Dirigés 10 h
En savoir plusTD UE3 Introduction to quantum field theory S0 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE4 Disordered systems S0 SM2NLP (Cours Magistral)15 h
- CM UE4 Disordered systems S0 SM2NLP (Cours Magistral)15 h
- TD UE4 Disordered systems S0 SM2NLP (Travaux Dirigés)10 h
- TD UE4 Disordered systems S0 SM2NLP (Travaux Dirigés)10 h
CM UE4 Disordered systems S0 SM2NLP
Cours Magistral 15 h
En savoir plusCM UE4 Disordered systems S0 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE4 Disordered systems S0 SM2NLP
Travaux Dirigés 10 h
En savoir plusTD UE4 Disordered systems S0 SM2NLP
Travaux Dirigés 10 h
En savoir plus
UE1 Systems of electrons S0 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the theory of high-density electron gas.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: quantum mechanics, statistical physics
Topics of the course: Electron liquids, approximations of Hartree and Hartree-Fock, random phase approximation, Landau theory of Fermi liquids, Luttinger liquid, Tomonaga-Luttinger model. Mott transitions, Mott insulators, Wigner crystal, Hubbard model.
Skills to be achieved:
Understanding the basic features of the degenerate Fermi systems.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE2 Introduction to astrophysics and cosmology S0 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the applications of particle physics in astrophysics and cosmology.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: quantum mechanics, General Relativity
Topics of the course: Primordial universe and its expansion, nucleosynthesis and baryogenesis,
dark matter and dark energy, compact astrophysical objects and gamma-ray bursts, cosmic rays.
Skills to be achieved:
Understanding the basic features of the cosmological evolution.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE3 Introduction to quantum field theory S0 SM2NLP
UE 25 h - 5 Crédits ECTS
bjectives: Introduction to the concepts and methods of modern quantum field theory.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: quantum mechanics
Topics of the course: Canonical quantization of a free field, scalar field, spinor field, gauge field. Perturbation theory, Feynman diagrams, quantum electrodynamics, cross section, Compton effect. Renormalization, divergencies and contra-terms.
Skills to be achieved:
Ability to carry out perturbative calculations in the tree approximation.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE4 Disordered systems S0 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the theory of complex condensed matter systems.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: quantum mechanics, statistical physics
Topics of the course: Random field, random potential, spin glasses, non-ergodic behavior. Localization, density of states, spread and localized states, Anderson model, one-dimensional gas. Disordered elastic systems, correlation functions, vortex lattice in superconductors. Frustrated spin systems.
Skills to be achieved:
Understanding the basic principles of description of disordered systems.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
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- CM UE1 Systems of electrons S0 SM2NLP (Cours Magistral)15 h
- CM UE1 Systems of electrons S0 SM2NLP (Cours Magistral)15 h
- TD UE1 Systems of electrons S0 SM2NLP (Travaux Dirigés)10 h
- TD UE1 Systems of electrons S0 SM2NLP (Travaux Dirigés)10 h
CM UE1 Systems of electrons S0 SM2NLP
Cours Magistral 15 h
En savoir plusCM UE1 Systems of electrons S0 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE1 Systems of electrons S0 SM2NLP
Travaux Dirigés 10 h
En savoir plusTD UE1 Systems of electrons S0 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE2 Introduction to astrophysics and cosmology S0 SM2NLP (Cours Magistral)15 h
- CM UE2 Introduction to astrophysics and cosmology S0 SM2NLP (Cours Magistral)15 h
- TD UE2 Introduction to astrophysics and cosmology S0 SM2NLP (Travaux Dirigés)10 h
- TD UE2 Introduction to astrophysics and cosmology S0 SM2NLP (Travaux Dirigés)10 h
CM UE2 Introduction to astrophysics and cosmology S0 SM2NLP
Cours Magistral 15 h
En savoir plusCM UE2 Introduction to astrophysics and cosmology S0 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE2 Introduction to astrophysics and cosmology S0 SM2NLP
Travaux Dirigés 10 h
En savoir plusTD UE2 Introduction to astrophysics and cosmology S0 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE3 Introduction to quantum field theory S0 SM2NLP (Cours Magistral)15 h
- CM UE3 Introduction to quantum field theory S0 SM2NLP (Cours Magistral)15 h
- TD UE3 Introduction to quantum field theory S0 SM2NLP (Travaux Dirigés)10 h
- TD UE3 Introduction to quantum field theory S0 SM2NLP (Travaux Dirigés)10 h
CM UE3 Introduction to quantum field theory S0 SM2NLP
Cours Magistral 15 h
En savoir plusCM UE3 Introduction to quantum field theory S0 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE3 Introduction to quantum field theory S0 SM2NLP
Travaux Dirigés 10 h
En savoir plusTD UE3 Introduction to quantum field theory S0 SM2NLP
Travaux Dirigés 10 h
En savoir plus -
- CM UE4 Disordered systems S0 SM2NLP (Cours Magistral)15 h
- CM UE4 Disordered systems S0 SM2NLP (Cours Magistral)15 h
- TD UE4 Disordered systems S0 SM2NLP (Travaux Dirigés)10 h
- TD UE4 Disordered systems S0 SM2NLP (Travaux Dirigés)10 h
CM UE4 Disordered systems S0 SM2NLP
Cours Magistral 15 h
En savoir plusCM UE4 Disordered systems S0 SM2NLP
Cours Magistral 15 h
En savoir plusTD UE4 Disordered systems S0 SM2NLP
Travaux Dirigés 10 h
En savoir plusTD UE4 Disordered systems S0 SM2NLP
Travaux Dirigés 10 h
En savoir plus
UE1 Systems of electrons S0 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the theory of high-density electron gas.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: quantum mechanics, statistical physics
Topics of the course: Electron liquids, approximations of Hartree and Hartree-Fock, random phase approximation, Landau theory of Fermi liquids, Luttinger liquid, Tomonaga-Luttinger model. Mott transitions, Mott insulators, Wigner crystal, Hubbard model.
Skills to be achieved:
Understanding the basic features of the degenerate Fermi systems.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE2 Introduction to astrophysics and cosmology S0 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the applications of particle physics in astrophysics and cosmology.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: quantum mechanics, General Relativity
Topics of the course: Primordial universe and its expansion, nucleosynthesis and baryogenesis,
dark matter and dark energy, compact astrophysical objects and gamma-ray bursts, cosmic rays.
Skills to be achieved:
Understanding the basic features of the cosmological evolution.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE3 Introduction to quantum field theory S0 SM2NLP
UE 25 h - 5 Crédits ECTS
bjectives: Introduction to the concepts and methods of modern quantum field theory.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: quantum mechanics
Topics of the course: Canonical quantization of a free field, scalar field, spinor field, gauge field. Perturbation theory, Feynman diagrams, quantum electrodynamics, cross section, Compton effect. Renormalization, divergencies and contra-terms.
Skills to be achieved:
Ability to carry out perturbative calculations in the tree approximation.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
UE4 Disordered systems S0 SM2NLP
UE 25 h - 5 Crédits ECTS
Objectives: Introduction to the theory of complex condensed matter systems.
En savoir plus
Organization: CM: 15 h, TD: 10 h.
Necessary background: quantum mechanics, statistical physics
Topics of the course: Random field, random potential, spin glasses, non-ergodic behavior. Localization, density of states, spread and localized states, Anderson model, one-dimensional gas. Disordered elastic systems, correlation functions, vortex lattice in superconductors. Frustrated spin systems.
Skills to be achieved:
Understanding the basic principles of description of disordered systems.
Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%
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UE au choix
UE au choix
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- UE5 Stage 3 mois S0 SM2NLP (UE)3 h - 20 Crédits ECTS
Enseignements
- 10 Crédits ECTS
En savoir plusUE5 Stage 3 mois S0 SM2NLP
UE 3 h - 20 Crédits ECTS
Objectives: Students have to accomplish a 3-month internship in a research lab in France.
En savoir plus
During this time they will work on a particular research problem under a supervision of a specialist in the lab. The results of this work will be presented in the form of a diploma theses to be defended in front of the pedagogic commission.
Grading plan:
Session 1: Written report and the oral presentation (ET) 100 %
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S1
S1 : Semestre 7 S7 SM1NLP
S2
S2 : Semestre 8 S8 SM1NLP
S4
Et après ?
Niveau de sortie
Compétences visées
URL Fiche RNCP
Poursuites d'études
Débouchés professionnels
Secteurs d'activité ou type d'emploi
- Recherche scientifique et technique
- Enseignement
- Études et conseils
Types d'emploi :
- Chercheur, Enseignant-chercheur
- Ingénieur recherche-développement
- Ingénieur d’études
- Professeur Agrégé ou Certifié